We consider a disturbance force model in Laplace domain as \(F^d(s) = \frac{\alpha s}{s+\omega _p}\) , where \(\alpha \)  and \(\omega _p\)  adjust the magnitude and cut-off frequency. This disturbance results in robot position deviation according to the admittance dynamics \(X^d(s) = A(s)F^d(s)\) , where \(A(s) = (M_is^2+D_is+K_i)^{-1}\) . Recall the equivalency of the two-norm in time and Laplace domain, \(\Vert x^d(t) \Vert ^2_2= \Vert X^d(s) \Vert ^2_2\)  by Parseval's theorem [1]}, and that \(\Vert X^d(s) \Vert _2^2\)  can be found by the observability grammian as
\(\Vert X^d(s) \Vert ^2_2 & = & B_d^T X_o B_d,  \\\mathrm {where}& & A_dX_o +X_oA_d^T = C_d^TC_d, \) 
